Insect-based products are novel foods (NF) that merit careful study. For this reason, in this work a method has been developed for the simultaneous analysis of four food processing contaminants (FPC), acrylamide (AA), 5-hydroxymethylfurfural, (HMF), 5-methylfurfural (MF) and furfural (F), in insect-based products (bars, crackers and flours) by high-performance liquid chromatography coupled to triple quadrupole mass spectrometry (HPLC-QqQ-MS/MS). The method consisted of a solid-liquid extraction (SLE) with acidified water, followed by solid-phase extraction (SPE), using 100 mg of a sorbent based on mesostructured silica with a large pore functionalized with amino groups (SBA-15-LP-NH2). The analytical method was properly optimized and validated in a representative bar sample of pineapple & coconut with cricket flour (Ins-B-Pine-Coco) showing good accuracy, with recoveries ranging from 70–101% for the four analytes and adequate precision (RSD < 9%). Good linearity (R2 ≥ 0.995) and low method quantification limits for AA (between 1.3–1.4 µg/g), F (between 7.9–8.8 µg/g), MF (between 3.1–6.5 µg/g) and HMF (between 1.5–3.3 µg/g) were also obtained in all samples studied. The proposed method was successfully applied in eleven insect-based foods. Results revealed that insect-based bars can be a good alternative to traditional cereal bars to reduce dietary exposure to HMF; but, in order to reduce the exposure to AA, alternative formulations must be evaluated in the design of innovative insect-based crackers.